LP (2003) 1 OPERATIONS RESEARCH: 343 1. LINEAR PROGRAMMING 2. INTEGER PROGRAMMING 3. GAMES Books: Ð3Ñ IntroÞ to OR ÐF.Hillier & J. LiebermanÑ; Ð33Ñ OR ÐH. TahaÑ; Ð333Ñ IntroÞ to Mathematical Prog ÐF.Hillier & J. LiebermanÑ; Ð3@Ñ IntroÞ to OR ÐJ.Eckert & M. KupferschmidÑÞ LP (2003) 2 LINEAR PROGRAMMING (LP) LP is an optimal decision making tool in which the objective is a linear function and the constraints on the decision problem are linear equalities and inequalities. It is a very
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An Introduction to Linear Programming Steven J. Miller∗ March 31‚ 2007 Mathematics Department Brown University 151 Thayer Street Providence‚ RI 02912 Abstract We describe Linear Programming‚ an important generalization of Linear Algebra. Linear Programming is used to successfully model numerous real world situations‚ ranging from scheduling airline routes to shipping oil from refineries to cities to finding inexpensive diets capable of meeting the minimum daily requirements. In many of these problems
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European Journal of Operational Research 217 (2012) 519–530 Contents lists available at SciVerse ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor Production‚ Manufacturing and Logistics Optimizing system resilience: A facility protection model with recovery time Chaya Losada‚ M. Paola Scaparra ⇑‚ Jesse R. O’Hanley Kent Business School‚ University of Kent‚ CT2 7PE Canterbury‚ UK a r t i c l e i n f o Article history: Received
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BSTA 450 - Review Sheet - Test 2 1. Consider the following linear programming problem: Maximize Z = 400 x + 100y Subject to 8 x + 10y ≤ 80 2 x + 6y ≤ 36 x≤ 6 x‚ y ≥ 0 BSTA 450 Find the optimal solution using the graphical method (use graph paper). Identify the feasible region and the optimal solution on the graph. How much is the maximum profit? Consider the following linear programming problem: Minimize Z = 3 x + 5 y (cost‚ $) subject to 10 x + 2 y ≥ 20 6 x + 6 y ≥ 36 y ≥ 2 x‚ y ≥ 0 Find
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Unit 1 Lesson 9 : The Big M Method Learning outcomes • The Big M Method to solve a linear programming problem. In the previous discussions of the Simplex algorithm I have seen that the method must start with a basic feasible solution. In my examples so far‚ I have looked at problems that‚ when put into standard LP form‚ conveniently have an all slack starting solution. An all slack solution is only a possibility when all of the constraints in the problem have or = constraints‚ a starting basic
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MERTON TRUCK COMPANY 1) No. of Model 101= x‚ no. of model 102=y.Unit contribution/model= S.P – (Variable costs + Fixed cost).For Model 101‚ variable cost=36000 /unit‚For Model 102‚ variable cost=33000/unit.Fixed cost for both the model= 8600000 Therefore‚ total contribution z=39000x+38000y-36000x-33000y-8600000Z=3000x+5000y-8600000 The Constraints are:Engine assembly: x + 2y <= 4000Metal stamping: 2x + 2y <=6000Model 101 assembly: 2x <=5000Model 102 assembly: 3y <= 4500x‚y>=0.Solving
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Mathematical Models Contents Definition of Mathematical Model Types of Variables The Mathematical Modeling Cycle Classification of Models 2 Definitions of Mathematical Model Mathematical modeling is the process of creating a mathematical representation of some phenomenon in order to gain a better understanding of that phenomenon. It is a process that attempts to match observation with symbolic statement. A mathematical model uses mathematical language to describe a system. Building a
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Case Study: RED BRAND CANNERS Vice President of Operations Mr. Michell Gorden Controller Mr. William Copper Sale Manager Mr. Charles Myers Production Manager Mr. Dan Tucker Purpose: Decide the amount of tomato products to pack at this season. Tomato Products Whole Tomato Tomato Juice Tomato Paste Information: 1. Amount of Tomato: 3‚000‚000 pounds to be delivered. Tomato quality: 20% (grade A) × 3‚000‚000 = 600‚000 pounds 80% (grade B) × 3‚000‚000 = 2‚400‚000 pounds (provided by production
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Julia’s Food Booth. Parts A thru C. Please provide linear programming model‚ graphical solution‚ sensitivity report‚ and answers to questions A thru C. (Problem on page 2) [pic] [pic] A) Formulate and solve a linear programming model for Julia that will help you advise her if she should lease the booth. Let‚ X1 =No of pizza slices‚ X2 =No of hot dogs‚ X3 = barbeque sandwiches Formulation: 1. Calculating Objective function co-efficients:
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Linear Programming Application Transportation Problem The Navy has 9‚000 pounds of material in Albany‚ Georgia that it wishes to ship to three installations: San Diego‚ Norfolk‚ and Pensacola. They require 4‚000‚ 2‚500‚ and 2‚500 pounds‚ respectively. Government regulations require equal distribution of shipping among the three carriers. The shipping costs per pound for truck‚ railroad‚ and airplane transit are shown below. Formulate and solve a linear program to determine the shipping
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